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Redshift space distortion (RSD) observed in galaxy redshift surveys is apowerful tool to test gravity theories on cosmological scales, but thesystematic uncertainties must carefully be examined for future surveys withlarge statistics. Here we employ various analytic models of RSD and estimatethe systematic errors on measurements of the structure growth-rate parameter,$f\sigma_8$, induced by non-linear effects and the halo bias with respect tothe dark matter distribution, by using halo catalogues from 40 realisations of$3.4 \times 10^8$ comoving $h^{-3}$Mpc$^3$ cosmological N-body simulations. Weconsider hypothetical redshift surveys at redshifts z=0.5, 1.35 and 2, anddifferent minimum halo mass thresholds in the range of $5.0 \times 10^{11}$ --$2.0 \times 10^{13} h^{-1} M_\odot$. We find that the systematic error of$f\sigma_8$ is greatly reduced to ~5 per cent level, when a recently proposedanalytical formula of RSD that takes into account the higher-order couplingbetween the density and velocity fields is adopted, with a scale-dependentparametric bias model. Dependence of the systematic error on the halo mass, theredshift, and the maximum wavenumber used in the analysis is discussed. We alsofind that the Wilson-Hilferty transformation is useful to improve the accuracyof likelihood analysis when only a small number of modes are available in powerspectrum measurements.

On the Systematic Errors of Cosmological-Scale Gravity Tests using Redshift Space Distortion: Non-linear Effects and the Halo Bias